Solve for $x$ and $y$ using elimination. ${3x-3y = 18}$ ${-6x-4y = -56}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $2$ ${6x-6y = 36}$ $-6x-4y = -56$ Add the top and bottom equations together. $-10y = -20$ $\dfrac{-10y}{{-10}} = \dfrac{-20}{{-10}}$ ${y = 2}$ Now that you know ${y = 2}$ , plug it back into $\thinspace {3x-3y = 18}\thinspace$ to find $x$ ${3x - 3}{(2)}{= 18}$ $3x-6 = 18$ $3x-6{+6} = 18{+6}$ $3x = 24$ $\dfrac{3x}{{3}} = \dfrac{24}{{3}}$ ${x = 8}$ You can also plug ${y = 2}$ into $\thinspace {-6x-4y = -56}\thinspace$ and get the same answer for $x$ : ${-6x - 4}{(2)}{= -56}$ ${x = 8}$